Nuprl Lemma : ratreal-int-rat-mul
∀[a:ℤ × ℕ+]. ∀[n:ℤ]. (ratreal(int-rat-mul(n;a)) = n * ratreal(a))
Proof
Definitions occuring in Statement :
int-rat-mul: int-rat-mul(n;x),
ratreal: ratreal(r),
int-rmul: k1 * a,
req: x = y,
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
product: x:A × B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
implies: P ⇒ Q,
all: ∀x:A. B[x],
squash: ↓T
Lemmas referenced :
sq_stable__req,
ratreal_wf,
int-rat-mul_wf,
int-rmul_wf,
istype-int,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality_alt,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
independent_functionElimination,
lambdaFormation_alt,
because_Cache,
imageMemberEquality,
baseClosed,
imageElimination,
equalityIstype,
dependent_functionElimination,
productIsType,
universeIsType
Latex:
\mforall{}[a:\mBbbZ{} \mtimes{} \mBbbN{}\msupplus{}]. \mforall{}[n:\mBbbZ{}]. (ratreal(int-rat-mul(n;a)) = n * ratreal(a))
Date html generated:
2019_10_30-AM-09_24_19
Last ObjectModification:
2019_01_11-AM-10_13_03
Theory : reals
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